The specifics of the CONSCAN, including calibration, signal cleanup, and system protection are presented. The CONSCAN was previously recommended for implementation in the antenna control assembly. Equations for programming the algorithms are provided. The described treatment is designed to lead to developing K-band. The recommended techniques to be employed in conjunction with CONSCAN are summarized: (1) for initial acquisition, employ stepped spiral search; (2) employ continued and incessant testing of signals to verify: in-lock, reasonable in level, and within limits; (3) use FFT for signal processing if feasible, as it provides more tests and insight into existence of glitches and spurious content of the input signal level

Abichandani, K. P.

Ohlson, J. E.

English

NASA Technical Reports Server

TDA PmgresS Report 42-70 
t; 
May and June 198e 
CONSCAN Implementation for Antenna Control Assembly 
J. E. Ohlson 
Stanford Telecommunications Inc. 
and 
K. P. Abichendani 
DSN Engineering Section 
CONSCAN was previously recommended for implementation in the Antenna Control 
Assembly. This article presents specifics of this implementation, including calibration. 
s@al cleanup, am* system protection Equations for programming the algorithms are 
provided. 
1. Introduction E(k) = elevation deviation 
Reference I discussed the merits of several automatic track- 
ing techniques, and concluded that CONSCAN (conical-scan 
tracking) was most desirable for DSN antenna application. 
X(k) = cross-elevation deviation 
A(k) = azimuth deviation (or hour-angle deviation) 
EANT = antenna elevation (or declination) 
A,,NT = antenna azimuth Additional effort was necessary to  develop the equations 
and algorithms required for the implementation of CONSCAN. 
This article provides that detail as the final phase of the study 
involving automatic tracking techniques for the Antenna Con- 
trol Assembly (ACA). 
To maintain crosselevation deviation constant with elevation, 
the azimuth deviation must vary with elevation angle: 
(1 )  
This report presents the detailed analysis and instructions 
A ( k )  = X(k)sec EANT for implementing CONSCAN into the ACA. 
From Fig. 1, the scan equations are II. CONSCAN Algorithm 
Scan Jenation may be defined as deviation of the antenna 
h e m  axis from tlic antenna borcsigtit axis. The deviation is 
resolved into two orthogonal components called elevation and 
crosselevatmn. Le! 
E(k) = R sin w k A 
X ( k )  = R cos w k A 
(2, 
(3 )  
153 
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o = scan rate in radjs 
= ZnlP 
P = scan period,s 
R = scarl radius, deg (Fw. I )  
R = no. of units of A (constant) 
A = time between updates (for data samples) 
where E, and X, are the latest (kth) correction in elevation 
and cresselevation, respectively. The predicts for azimuth and 
elevation are calculated from the spacecraft ephemeris or from 
the known location of a radio star. The Correction Table is a 
set of stored corrections and provides a fmt-order correction 
to previously measured systematic errors. 
Hence, having chosen the time between updates, and indexing 
time by the number R, the scan deviation may readily be 
computed. 
Iv. COOtdinate --On Algorithm 
Reference 2 derives the expressions for corrections in each 
coordinate. These corrections are given in i n t e p l  form, but 
are modified to conform to digital processing requirements by 
expressing them in summation form as follows, 
111. Antenna Pointing Angle Equations 
The components of the antenna pointing angles, E A m ,  
and A A N T  are calculated for two cases, CONSCAN OFF and 
ON. (Refer to Fig. 2 )  
Ec = G V(k)sin(okA+Z) (8) 
SCAN k (1) With CONSCAN OFF, 
= EpRED(k) ' ETAB(&) "E (4) 
Xc = C v(kjcos(ORA+Z) (9) 
AAm(k)  ApRED(R)+ATAB(R)+SA ( 5 )  SCAN k 
where the subscripts are where V ( R )  is the kth edited signal sample, 
ANT = actual antenna command 
PRED = predicted value from ephemerides 
G = g a i n  
2 = phaseshift 
TAB = value from systematic error correction table The phase shift 2 is required because of mechanical phase 
lag of the antenna response and the phase lag of the AGC or 
radiometer averaging. The gain G and the phase shift 2 must 
be calibrated for each antenna configuration and signal source. 
The values of E ,  and X, may be determined by one of the 
(1) Brute Force correlation. 
(2) Fast Fourier transform. 
The Brute Force approach is simple and is indicated !J> the 
nature of expression. All that is needed is use of a sine and 
cosine lookup table, multiplication, and accumulation. 
and where, 
SE = total correction for elevation 
SA = total correction for azimuth following approaches: 
= s, sec &(k) 
Sx = total correcti( rl for crosselevation 
( 2 )  With CONSCAN ON, 
(6) EANT(k) = EpRED + E,,(&) + s, + EJk) 
The fast Fourier transform (FFT). although it requires 
more computations, provides more information as a bonus. A,,vT(k) = +A, , (k )+SA + A c ( k )  
Analytically, the resultant correction parameter P, having two 
components X, and E,, is expressed as 
where j is the square root of - 1. If we use Eqs. (8) and (9) and 
DeMoivres theorem, 
This is the Y(1) term of the discrete Fourier transform, gener- 
ally computed by the FFT. The transform is 
The term Y( 1) gives pointing error. AU terms for N > 1 are a 
measure of anomalies. For example. ellipticity it! the antenna 
beam will give a very small but finite contribution io Y(2). 
Normally, all Y(N)  for N 2 2 will be very small because V(k) is 
usually nearly constant. When V(k) has a glitch due to receiver 
dropout, interference, or a step change of signal such as a 
spacecraft transmitter mode change, then Y(N) for N 2 2 can 
be much larger than Y(l). Thresholding can be done on a few 
values of Y(N) to detect anomalous conditions in order to 
reject potentially absurd calculated “corrections.” 
The number of signal samples per scan must be chosen to 
be a power of 2 in order to directly usc the FFT. For example, 
the conveniently sized 5 12-point FFT provides a scan of 5 1.2 s 
when a signal sample rate of 10 Hz is used. 
The steps followed in using the FFT are: 
(1) Using the V(k) values for a scan, calculate Y(N) by 
perfomhg the above summation (Eq. 12), for several 
values of N, say 2,3,  and 4. 
(2) Compare each Y(N) thus computed to preaelected 
threshold. If the threshold is exceeded, the correction 
for this scan is rejected. The threshold that is chosen 
should be small; it should be on the ortier of the scan 
radius. However, it should be large enough to allow the 
second harmonic gnerated as a result of elliptic cross 
section of the beam to be ignored. The rejection rate 
due to glitches and other spurious content of Y(N) 
should be less than 5 percent. 
V. Tracking Signal Cleanup and PmWctlon 
D W T n r C k  
Reference 1 proposed signal cleanup and protection 
schemes both for radio sources and spacecraft. 
The signal inputs are (1) square law detector output far 
for spacecraft tracking. The anomauBs that are b l y  to occur 
radio sources and (2) AGC (Automatic Gaia Control) voltage 
that will affect the received signal power may 2 listed as 
follows: 
Signal dropout due to momentary receiver dropout 
(out-oNock), operator error or some unexpected tran- 
sient (glitch) in the receiving system. 
Change in spacecraft transmitter or antenna mode. 
Spacecraft antenna pointing direction change with 
spacecraft limit cycling, or some other change on board 
the spacecraft causing variation in the downlink @pal 
strength. 
In the case of spinstabilized spacecraft, modulation in 
the signal level due to spin rate. 
Testing is a very essential part of Qpal processlog. since 
the data processing requirements are low and the penalty for 
spacecraft data loss is high, tests should be made as frequently 
as possible. 
When track-g radio sources, a single receiver dropout 
should cause a scan correction to be skipped. Further, 
expected signal level should be compared to observed AGC 
level as another check. ACC can be calibrated at known Signal 
levels, and/or by feeding the expected signal level to ACA. The 
apparent signal level is continuously compared with the 
expected (predicted) signal level, and, if deviation is greater 
than 1 or 2 dB, that scan is rejected. 
However, if there is a slow cycling of signal level, a straight 
line connecting t!e last and the first point may be subtracted 
to determine the difference in s i p l  le-el. 
Hence, ignore scan if 
I Y(k)  - expected V(k) I2 threshold (13) 
This is the condition of ou! nflock;ifcycling(low)isexpected, 
the straight line test referred to above is analytically expressed 
a, 
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where 
Th = threshold (1 or 2 dB) 
ko = number of points in scan 
For testing of radio source trscdng anomalies, the system 
temperature and the expected radio source temperature should 
be provided so a check can be run. This will entail a precise 
setup for the radiometer gain to ensure accurate comparisons. 
A table of temperatures for common radio stars could be 
easily stored into the system memory. 
If To is the system operating temperature and T, the radio 
source (xpected) temperature, the scan should be ignored if 
scaled [ V(k)] < Top 
scaled [ V(k)] > Top + T, + margin 
(1 5) 
(16) 
or 
There is the very real likelihood that, even though signal 
level is continuously and carefully tested, an unusually large 
correction may sneak through. Thus limit tests become neces- 
sary. These may be categorized as first limit and second limit. 
VI. 
First limit: If the desired correction exceeds the first 
limit, correction only to the extent of the limit value is 
to be made. Examples of limits that could he set as first 
limits on elevation and crosselevation are 
(a) For S-band, 0.01 5 deg 
(b) For X-band, 0.005 deg 
If the next correction has to be the same limit <because 
it is equaled or exceeded), no correction should be 
made; instead, a warning is generated. 
Second limit: If the desired correction exceeds the 
second limit, no correction is made; instead, a warning 
is generated. Example limits for elevation and cross- 
elevation that could be set are 
(.a) For S-band, 0.030 deg 
(b) For X-band, 0.010 deg 
Define 
where h in Ref. 2 has been defmed as ”selectable” gain snd P = 
2nIwm 
A is a parameter readily mesurable by use of expressions 
1 1  through 21 (Ref. 2). Equation (19) of Ref. 2 expresses it as 
(for radiometer) 
where C is a constant represcnting receiver gain, and B is the 
effective band width: 
with I HO l2 the pcwer gain, and 
Id? = -2 -
W 2  
R as used above is the scan radius and w is the antenna 
heamwidth between half power points. 
p = 4 In 2 = 2.773 (22) 
From Eq. (18) above, Antenna and Signal Source Gain and 
Phase Calibration 
In r  = Inti - hA) 2 -hA 
Referring t o  Eqs. (8) and (91, we see the gain parameter is 
given by G. At  tlus time. an expression for C will be derived to 
enable calibration. 
substituting in Eq. (1  7). 
The closed loop time constant T is gven by (Ref. 2) T = PIhA 
ORIGINAL PAGE IS 
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Thus, expressing G = hA after dropping the negative sign, 
Aw2 
KY3” T,R G (radiometer) 
For c acecraft, Ref. 2 (Eq. 101) has 
where k’ is found by calibration of the AGC slope. 
By using Eq. ( 2 5 )  and G = hA, 
2Aw2 G (spacecraft) = -k’pTR 
k’ may be calculated by using the derivation for fast AGC in 
Ref. 3, where in Eq. (1 2), the expression ‘to be used is 
1 
VAGC = -- In v ( r )  a 
where v ( r )  is the cormalized voltage gain (Eq. (63), Ref. 2), 
1 
k’  
u = -  
with R2, 0 2 ,  a2 << w: (Eq. (63), Ref. 2) using Eq. (91) of 
Ref. 2 .  and Eq. (26) above, 
a IS given in Eq. (3)  of Ref. 3, and 9, is the symbol for 
elevttion (crms-elevaiion) deviation in the kth scan. 
8.686 a = slope in dB/volt = S 
Equation ( 2 7 )  above can be rewritten by substituting k‘ from 
Eq.(3l)abuve.andD- 2.773 
Aw2 c = o.ox3os - R ( 3 2 )  
We will now discuss phase-shift calibration. Equations (8), 
(9). and (1 1) above include the phase term 2. The phase shift 
is needed because 
(1) For radio source tracking, fdtering in the radic neter 
causes a phase lag. 
(2) There is a filtering effeci of AGU, during spacecraft 
tracking. 
(3) Phase lag of the antenna is a function of t i e  scan 
period, e.g., for a 64-meter antenrs (Ref. 2) and 
(a) For a 284 scan, Z = -30 deg 
(b) For a 584 scan,Z=- 15 deg 
The required value of Z may be measured by rhe following 
means: 
(1) Assuming a nominal value of Z, CONSCAN the antenna 
to achieve boresight. 
(2) Open the control loop, and offset the antenna in one 
axis only, say crosselevation. 
(3) If the nominal Z is correct, the correlation and h e m  
the indicated correction will be nonzero in only the 
offset axis. 
(4) If Z is incorrect (i.e., if correlation is nonzero in both 
the axes), the correction for Z for the case of c r w -  
elevation offset is: 
elevation correction = tan-’ - 
crosselevation correction 
If the fast Fourier transform (FFT) is used for signal process- 
ing, the phase angle of the fundamental output Y( 1 ) is exactly 
AT. 
VII. Signal Source Acquisition Policy 
Predicted offset from boresight is expected to be within IO 
dB (X-band) initially. As this raises the possibility of large 
anomalies. 3 spiral scan f o r  acquisition is recommended. 
To attain higher accuracy in initial acquisition, three param- 
eters should be established. 
1 57 
QRIGINA'L FA& 12 
OF POOR QUALlW 
(1) Beamwidth B in which acquisition is highly likely. 
( 2 )  T i e  T necessary to make a decision. 
Another maybe simpler v ?y to a soluton is to implement 
Eq. ( 3 5 )  directly. Every T wconds, command a &an@ in 8 at 
the ratc 
(3) Size of the search region. 
The procedure for initial acquisition is as follows (Fig. 3): 
(1) Dwell a* best grwss for T seconds. 
(2)  Move out B/2 in one axis. 
WithAt=T,  
A0 B 
pt RT 
- z -  
(39) 
B R A t l a  R ~ T  = -  R (3) Dwell at that position for T wconds. 
(4) Traverse spiral until the search is complete (the spiral is 
discussed below). Using Eq. (33) now and substitilting F,q. (39), we ha* 
( 5 )  Set the scanner at the point of maximm signal level. 
Alternatively, one may stop when any signal is found: 
but this may be a side lobe. 
B= Ad = -B a=--.2n 2ItR 
The spiral search is done by arguing that for every 2n The response to comn&.?ds every T seconds can be prevented 
from being jerky by choosing TIN intervals instead of T,  with 
N such that smoothness results. Simubmeously, A0 and AR 
increase in 8 there should be an increase in R by B, Le., 
dR de 
B 2n 
- = -  
quantities can be attained in N steps. 
(33) 
The coordinate system is shown in Fig. 3a. 
VIII. Conclusions If the scan rate is 8, at R radiw of scan velocity is, 
This report is intmded to he the final one as regards 
investigation into CONSCAN and treatment cf appropriate 
algorithms for signal cleanup and limit tests to assure its 
maximum acciracy and desirability. 
(34) velocity = A d 
so if in T seconds the beam has moved by 3n amount B, then 
( R i ) T  = B 
solving q s .  (33) and (35), we have 
where 
d(0 )  = 0;  R ( 0 )  = R,, 
The treatment described herein is designed td lead to dev-I- 
opment of software for CONSCAN antenna operation includ- 
ing K band. Summarizing the recommended techniques to be 
employed in conjunction with CONSCAN: 
( I )  For initial acquisition, employ stepped spiral search. 
( 2 )  Employ continued and incessant testing of .... to 
!") 
verify: (36) 
(37) 
(a) In-lock. 
(b) Reasonable in level. 
(c) Within limits. 
(3) Use FFT for signal DTp.PE;..ig i:' ! r s . : ! + ,  E ;  at providei 
more test: 4 .,lsight into c ~ s k w - 5  of f j i t c ; ~ ~  and
spu.,' 'IIS content of the input signal level. 
158 
1. Abichsndani, K. P., and ohlsosl, J.  E., *'Boresight@ Techniques for the Antenna 
Control AsernMy (Am),'' TDA h g m s  Report 42-64. May and June 1981, Jet 
Propulsion Laboratory. Pasadena, California, August 15,1951. 
2. Ohlson, J. E., and Reid, M. S., h- lkking mdh the 64-&e:w4iumeim 
A n t m  at Gokhtm, T e ~ h n i d  h F v . 3  32-1605, Jet ~ @ P U ~ ~ O I I  hbontoiy. PdSa- 
&M. California. October I ,  1976. 
Cornwwnkxiwns, Vol. COM-22, No. 1 ,  pp. 72-75, January 1974. 
3. 0 l .b .  J. E.. "Exact Cynamics of Automatic Gain Contrd," IEEE ? h ~ ~ ~ ~ ~ i o n s  on 
1 59 
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PREDICTS CORRECTION 
TABU 
flg. 2. B W  dlagrun ol CONSCAN polntlng 


CONSCAN implementation for Antenna Control Assembly

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